Mangrove Tidal Exchange

What is modelled

A mangrove basin of area A is joined to the sea by a creek of length L and cross-section Ac. The sea level rises and falls with the tide; the water in the creek is pushed by the level difference and slowed by friction, which the roots increase. The volume that enters on a flood tide is the tidal prism. A well-mixed salt balance for the basin shows how far the river water dilutes it.

Equations

• Creek momentum (L / g Ac) dQ/dt = ηsea − ηbasin − k |Q| Q, with k = Cd L / (g h Ac²) and Cd = 0.003 + 0.01 × roots.
• Basin volume A dη/dt = Q + Qriver.
• Salinity V dS/dt = Q+(Ssea − S) − Qriver S.
• Basin to creek resonance T = 2π √(A L / g Ac); flushing time by the prism method V Ttide / P.

Checks run in the page

• Water balance over a tide.
• Linear-friction limit against the closed-form amplitude.
• Basin resonance period against the Helmholtz formula.
• Salt balance over 24 tides.

Honest simplifications

The basin has vertical walls and a flat bed (so the area does not change with level), the creek is one uniform channel with a single drag coefficient, the basin is perfectly mixed, there is no wetting and drying, no dispersion in the creek and no evaporation or rain. Real mangrove flats are shaped, vegetated and stratified, and the roots are counted only as extra drag in the creek.

• Press Dense roots and watch the tidal prism drop as the roots slow the creek flow.
• Press Narrow long creek and see the tide inside the basin lag and shrink.
• Press Flood season and see the river push the basin salinity far below the sea value.